Chapter 6.4, Problem 36PE

The magnitude of a star named Delta Cuphea varies from an apparent magnitude of $3.6$ to an apparent magnitude of $4.3$ with a period of $5.4$ days. At $t=0$ days, the star is at its brightest with a magnitude of $3.6$ (on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Write a simple harmonic motion model to describe the magnitude $M$ of the star for day $t$ .